Meteoritics & Planetary Science 38, Nr 6, 905–925 (2003) Abstract available online at http://meteoritics.org

Bolides in the present and past martian atmosphere and effects on cratering processes

Olga POPOVA,1* Ivan NEMTCHINOV,1 and William K. HARTMANN2

1Institute for Dynamics of Geospheres, Russian Academy of Sciences, Leninsky Prospekt 38, Building 1, 119334, Moscow, Russia 2Planetary Science Institute, 620 North 6th Avenue, Tucson, Arizona 85705, USA *Corresponding author. E-mail: [email protected] (Received 16 July 2002; revision accepted 29 April 2003)

Abstract–We investigate the action of the martian atmosphere on entering meteoroids for present and past atmospheres with various surface pressures to predict the smallest observable craters, and to understand the implications for the size distributions of craters on Mars and meteoroids in space. We assume different strengths appropriate to icy, stone, and iron bodies and test the results against available data on terrestrial bolides. Deceleration, ablation, and fragmentation effects are included. We find that the smallest icy, stone, and iron meteoroids to hit the martian ground at crater forming speeds of ≥500 m/s have diameters of about 2 m, 0.03–0.9 m (depending on strength), and 0.01 m, respectively, in the current atmosphere. For hypothetical denser past atmospheres, the cutoff diameters rise. At a surface pressure of 100 mb, the cutoff diameters are about 24 m, 5–12 m, and 0.14 m for the 3 classes. The weaker stony bodies in the size range of about 1–30 m may explode at altitudes of about 10–20 km above the ground. These figures imply that under the present atmosphere, the smallest craters made by these objects would be as follows: by ice bodies, craters of diameter (D) ~8 m, by stones about 0.5–6 m, and by irons, about 0.3 m. A strong depletion of craters should, thus, occur at diameters below about 0.3 m to 5 m. Predicted fragmentation and ablation effects on weak meteoroids in the present atmosphere may also produce a milder depletion below D ~500 m, relative to the lunar population. But, this effect may be difficult to detect in present data because of additional losses of small craters due to sedimentation, dunes, and other obliteration effects. Craters in strewn fields, caused by meteoroid fragmentation, will be near or below present-day resolution limits, but examples have been found. These phenomena have significant consequences. Under the present atmosphere, the smallest (decimeter-scale) craters in sands and soils could be quickly obliterated but might still be preserved on rock surfaces, as noted by Hörz et al. (1999). Ancient crater populations, if preserved, could yield diagnostic signatures of earlier atmospheric conditions. Surfaces formed under past denser atmospheres (few hundred mbar), if preserved by burial and later exposed by exhumation, could show: a) striking depletions of small craters (few meter sizes up to as much as 200 m), relative to modern surfaces; b) more clustered craters due to atmospheric breakup; and c) different distributions of meteorite types, with 4 m to 200 m craters formed primarily by irons instead of by stones as on present-day Mars. Megaregolith gardening of the early crust would be significant but coarser than the gardening of the ancient lunar uplands.

BACKGROUND: SIZE DISTRIBUTION OF SMALL From this, Shoemaker (1965) concluded that the steep branch CRATERS ON MARS was due to secondary debris being thrown out of lunar craters and falling back on the lunar surface. Neukum and Ivanov On each planetary body, the smallest craters (D <1 km) (1994) found moderate crater densities with a steep branch offer a special challenge. In the 1960s, the Ranger probes (slope ~−3.4) among craters of 200 m asteroids.

905 © Meteoritical Society, 2003. Printed in USA. 906 O. Popova et al.

The steep slope of the size distribution among small strongest chondrites was much higher than realistic. bodies implies large numbers of them hitting planetary Nemtchinov and Shuvalov (1992) estimated the sizes of the bodies, consistent with the rain of meter-scale and sub-meter- smallest bolides hitting the surface of Mars at hypervelocity scale meteorites entering the earth’s atmosphere. Shoemaker and estimated meteoroid diameters of 3 cm and 10 cm for (1965), thus, hypothesized that the extremely large numbers stones and icy bodies, respectively, suggesting that the cutoff of small impactors create a gardening effect that fragmented of smallest impact craters on Mars should be of the order 0.5 the lunar surface layers and produced a roughly 10 m deep to 2 m. Vasavada et al. (1993) improved the treatment of layer of a regolith since the lunar maria formed. This deceleration of bolides by various atmospheres with time- explanation of regolith has been generally accepted. varying properties. Independently, Hartmann et al. (1994) and The earth’s atmosphere causes dramatic breakup and loss Hartmann and Engel (1994) attempted estimates of the of small bolides and small craters. The luminous and fragmentation during bolide/atmosphere interaction with the explosive phenomena of meteoroids passing through present and past martian atmospheres. Their main interest was atmospheres lead to some confusion of nomenclature. Here, the atmosphere pressure needed to disrupt various taxonomic we follow the Encyclopedia of Astronomy and Astrophysics types of meteoritic bolides, and they concluded that at (Murdin 2001) in noting that “meteoroid” generally refers to pressures above a few hundred mbar, smaller stony and icy relatively small debris (sub-meter scale in some usages and meteorites would break up, leaving only craters caused by tens of meters in others) in interplanetary space that enters irons at sizes below about 0.5 to 4 km. Their additional atmospheres; “meteor” refers to the “transient luminous unpublished results were consistent with modern-day craters phenomena visible in the night sky” and generally implies down to about 1 m diameter, from both stony and iron bolides, small meteoroids; and “bolide” refers to “a bright meteor” that under the current atmosphere. Meanwhile, Rybakov et al. can involve explosions and meteorite fragments. The objects (1997) and Nemtchinov et al. (1998, 1999a) suggested that that create the smallest martian craters are generally in the small impactors may eject large amounts of dust into the latter size range and would be perceived from the martian martian atmosphere and may even create local dust storm surface as bolides. We will refer to them as meteoroids or, in conditions. recognition of the atmospheric effects, bolides. In 1997–98, Mars Global Surveyor (MGS) first revealed Mars presents an intermediate situation between the lunar a population of impact craters that appears relatively and Earth cases. On Mars, the effects of meter and sub-meter complete down to D <11 m (Malin et al. 1998; Hartmann et al. scale impactors have received surprisingly little attention, 1999), a finding not inconsistent with the above calculations. partly for historical reasons. Early flyby and orbiter missions The new data require a careful investigation of the smallest rarely resolved features much below 100 m in scale. Most bolides hitting the martian surface at hypervelocity (usually workers assumed qualitatively that the atmosphere blocked defined as >speed of sound in target materials) because such modest-scale bolides so that there would be no equivalent to impactors may have substantial effects. For example, Hörz et the finely gardened lunar regolith. This assumption was made al. (1999) pointed to an example of a possible meteorite- more quantitative by Gault and Baldwin (1970), who caused spall at 0.2 m scale on a rock in the Pathfinder lander predicted that the atmosphere would break up meteoroids of a images. In principle, this could have been caused by a size sufficient to make craters of diameter (D) <50 m. hypervelocity meteorite or by a larger fragment from a Another problem in the literature on small craters is that breakup event falling at a speed more like terminal velocity. the sub-km crater population was not widely studied because Hörz et al. (1999) also modeled martian atmospheric passage researchers focused on comparisons at multi-km scales of small meteoroids, taking into account ablation and drag, between crater populations on Mars and the outer planet but they did not take into account fragmentation (see below). satellites imaged by Voyagers 1 and 2 during the 1980s, where Precise estimates of the smallest impactors are important sub-km craters were usually not resolved. Furthermore, because the size distribution of small meteoroids increases at Tanaka (1986) defined the martian stratigraphic column (the a steep rate toward small diameters, and this means that a Noachian-Hesperian-Amazonian eras) only in terms of crater small decrease in the size of the smallest impactors has a large densities at scales of D = 1 to 20 km. Thus, for example, the effect in the number density of impacts and the timescale on major review article on martian cratering by Strom et al. which surfaces can be degraded by impact gardening. (1992) contained no crater count data on any martian craters This is not to say that wind transport, fluvial, and other smaller than 4 km even though Viking orbiters 15 years erosional processes do not dominate surface conditions but, earlier had shown craters down to the 100 m and less. rather, that small impacts could have additional Starting in the early 1990s, several workers began to consequences. An interplay, which depends on timescales, reassess small scale martian cratering. PadevÏt (1991) used exists between the exogenic and endogenic processes. For classical theory of meteors (Bronshten 1983) and predicted example, if an ancient fluvial episode left a lakebed deposit of penetration depths for various types of chondrites with carbonates and salts 1 cm thick, and if the timescale for weights in excess of 0.1 kg. His strength value for the impact gardening and erosion is much less than the likely Bolides in the present and past martian atmosphere 907 characteristic timescale for burial and preservation by Hartmann and Neukum 2001). Thus, the past martian windblown dust, then such deposits would likely have been atmospheric pressure has not necessarily been fixed at its broken up and diluted beyond MGS spectroscopic recognition current value. before they could be covered and preserved. New observations of atmospheric passage of relatively Hartmann et al. (2001) examined martian gardening big terrestrial meteoroids (1–10 m) allow more rigorous effects from the known crater statistics. Strictly on geometric treatment of martian bolides and understanding of small grounds of total areal crater coverage, and independent of any craters. In particular, many of these bolides (including the models of time dependent impact fluxes, he concluded that stones) were found to be weaker than previously assumed and mid-Hesperian surfaces have experienced coarse gardening to are disrupted in the earth’s atmosphere at altitudes of 25–40 a depth of some meters and Noachian surfaces to a depth of km. In the current martian atmosphere, some of these bodies tens of meters or (for the early Noachian) even hundreds of should be severely fragmented below an altitude of 15 km and meters. The idea of coarse gardening is independent of the reach the surface as a swarm of fragments (Nemtchinov et al. cutoff size of the smallest martian bolides because 100% of 1999b). Based on the above ideas, we have set the following the surface area, in regions older than mid Hesperian, has goals for this paper: been excavated by observable craters of D = 50 m. However, • Use modern modeling of bolide fragmentation to the meteoroid cutoff size will determine the degree of fine- determine the size of the smallest hypervelocity bolides scale gardening and erosion of rock surfaces, and this needs to to reach the martian surface under current atmospheric be better determined. Hartmann noted, for example, that conditions. preservation of thin, intact Noachian/Hesperian lakebed • Derive this result for each major meteoritic deposits would require burial during part or all of their history compositional class, ranging from weakly consolidated to protect them from the postulated gardening effects. A few carbonaceous and/or icy (cometary?) bodies through rare examples of such preserved surfaces may have been ordinary chondritic rocks to coherent iron meteorites. We recently exhumed, such as the Meridiani Terra hematite-rich note that the smallest objects to survive will be irons (as surface (Christensen et al. 2000; Hartmann 2001). This study on Earth). also noted that if the cutoff of smallest hypervelocity impact • Because irons constitute only a few percent of all craters is close to diameter (D) = 1 m in size, then martian meteoroids, investigate the offset in the crater diameter surfaces with crater densities less than ~1% of lunar mare distribution that should appear at the size reflecting crater densities (tens of Myr age, possibly found among the breakup and loss of the chondritic rock impactors, with youngest lava flows) would have negligible impact gardening the diameter distribution of craters due to irons extending because even the smallest impacts would not saturate the to smaller diameters, but at only a few percent of the surface. density at larger sizes. Due to oscillating obliquity (Ward 1992), Mars’ • Determine the same sets of results for hypothetical past atmosphere may vary over a modest range of surface martian atmospheres. pressures. The martian obliquity varied by as much as ~±20° • Study the disruption phenomena for fragmenting bolides and is characterized by 105-yr oscillations supplemented by and examine the question of the origin of martian crater 106-yr modulation of its amplitude (Ward 1992). These clusters pointed out by Hartmann and Engel (1994). oscillations cause variation of atmosphere density due to changes in insolation and ice stability. In principle, the record CRATER DIAMETER SCALING LAW AND of impact cratering could show evidence of the historical METEOROID VELOCITY DISTRIBUTION behavior of such changes in the planet atmosphere. Thicker transient atmospheres may also be produced for To study effects of atmosphere shielding, we must take a significant period of time by extensive volcanism on Mars. into account the efficiency of cratering at different impact Pollack et al. (1987) proposed that an early, wet martian velocities. A number of crater energy-diameter scaling laws climate was sustained by a thick CO2 atmosphere, and that can be found in Melosh (1989). The most widely used scaling extensive volcanism was the mechanism of CO2 recycling. law was proposed by Schmidt and Housen (1987) and may be Analysis of MGS images led to a conclusion by McEwen et written as al. (1999) that volcanism on early Mars was probably much 13⁄ 0.78 0.43 –0.22 more voluminous than previously documented and that it D= 1.16()ρm ⁄ ρt Dp ()Vsinθ g (1) must have affected the climate and near-surface environment. Moreover, martian rocks and crater counts provide evidence where D is the crater diameter (in m), Dp is the meteoroid for voluminous volcanism in the last quarter of martian diameter (in m), ρm and ρt are meteoroid and target densities, history (Nyquist et al. 2001; Hartmann et al. 1999; Hartmann V and θ are meteoroid velocity (in m/s) and angle from the and Neukum 2001). MGS images show fresh lava flows with horizontal, and g is the gravity acceleration (3.74 m/s2 for crater count model ages less than 100 Myr (Hartmann 1999; Mars). According to Christensen and Moore (1992), the bulk 908 O. Popova et al. density of martian surface materials is about 1.2–2.6 g/cm3, Craters of a given diameter (D) may be formed by the 3 and we will assume ρt = 2 g/cm here and below. impact of projectiles of somewhat different diameters, We assume Equation 1 between crater and projectile sizes depending on the impact velocity and impact angle (θ). Thus, may be used if the terminal velocity (Vt) ≥0.5 km/s, and we to derive size frequency distribution of craters, we sum the define this as the cutoff speed for formation of ordinary impact number of all projectiles with all possible velocities and craters. This speed depends somewhat on surface materials angles of impact. In differential form, this condition is and is not sharply defined. At lower speeds, the bolide falls to expressed as the ground and may partially or completely bury itself but νmax θmax does not create an explosion crater. In the limit of the lowest dN dN dD ------= d V dθ------p- fV()f()θ ∫ ∫  (3) terminal velocities, the “crater” is the size of the meteoroid dD dDp dD itself. This is somewhat idealized, but our goal here is to νmin θmin predict approximately the smallest high-speed impactors and dN the smallest recognizable craters that follow Equation 1. In where ------dDp reality, there will be a transition to smaller, lower velocity pits and rock spalls due to smaller, lower velocity meteoroids. is the size frequency distribution of projectiles (Ivanov 2001). Crater diameter is basically dependent on projectile energy. This equation allows us to construct a model impact crater The normalized distribution of atmospheric entry SFD. For asteroids and meteorites, data are often fitted for velocities at Mars (Bland and Smith 2000; Davis 1993; Flynn convenience by power law SFD, i.e., the differential and McKay 1990) is taken to be distribution in the form

V– 1.806 2 dN –k FV()= 0.0231 Vexp – ------(2) ------∼ D (4) 8.874 dD for V >5 km/s. The mean meteoroid velocity is estimated to where k may vary from 2.95 up to 3.5 (Ivanov 2001; be 10.2 km/s, and only a small fraction of bolides has entry Hartmann 1969) in the size range we primarily consider here. velocity in excess of 20 km/s. We assume that all types of An independent treatment comes from crater statistics meteoroids have the same atmospheric velocity. Higher (Hartmann 1969; Neukum and Ivanov 1994; Ivanov et al. average velocity of cometary material will result in more 2001; Neukum et al. 2001). The application of cratering dramatic fragmentation of cometary meteoroids. scaling laws permits authors to estimate the size frequency distribution of projectiles from the measured SFD of lunar CRATER DISTRIBUTION impact craters. Although this SFD can also be approximated in restricted size ranges by power law segments, Neukum has The shielding action of the martian atmosphere will developed a single polynomial fit that fits the SFD over a affect the craters’ size frequency distribution function (SFD). wider size range and is supported by data on several planetary The SFD has been presented several different ways in the bodies. The papers referenced above suggest that craters on literature. The cumulative distribution is the number of the moon and Mars were created by essentially the same craters/km2 (N) with diameter larger than a given diameter family of projectiles. (D) per unit area. It has the disadvantage of smoothing data We combine the above considerations with calculations on and not emphasizing sharp cutoffs in craters below certain atmospheric bolide passage to generate the SFD for the martian sizes where fragmentation may destroy meteoroids. The surface. Our estimates show that the angle of impact, differential distribution distributed as f(θ) ~sin(2θ), does not affect strongly the results except for extreme oblique impact. The effects of oblique dN ------impact are complicated, but these impacts have low probability, dD and we ignore them. On these grounds, we adopt the only a is the number of craters in the diameter range from D to D + mean value of impact angle θ (θ ~45°) here and below. δD divided by bin width δD. Another form of SFD To simplify the problem further, we use the velocity- presentation is the log-incremental representation with a average values of crater sizes < D > and omit the integration standard bin width in log D. If DL and DR are the left and the by velocity here. The simplified form of Equation 3 is as right bin boundaries, the standard bin width is DR/DL = 2 . follows: The last two systems show depletions at small sizes better than the cumulative system. The log-incremental distribution dN dN dD ------= ------p  (5) has the advantage that power-law segments have the same dD dDpd < D > slope as in the cumulative plot, and it was used by Hartmann and Berman (2000) to develop isochrons giving the martian Let us now consider the atmosphere action on entering SFD for different surface ages. bodies and its action on the resulting crater population. Bolides in the present and past martian atmosphere 909

INFLUENCE OF ATMOSPHERIC DECELERATION planet surface is shown in Fig. 1a. The surface pressures are AND ABLATION ON CRATERING labeled on the curves. The denser the atmosphere, the smaller the energy a given meteoroid retains on reaching the ground. The first atmospheric effect we consider is the For example, a 1 m H chondrite meteoroid in the present combination of deceleration and ablation. Vasavada et al. atmosphere keeps about 90–95% of its initial energy, but in a (1993) considered these effects martian atmospheres in the 300 mbar atmosphere, it keeps only few percent. From range of surface pressure 0.2–6 mbar and concluded that the deceleration and ablation effects alone, we can predict that production rates of cm-sized craters would be influenced by appreciable energy loss (>30%) in the present atmosphere the atmosphere pressure variations. We will primarily begins to occur only below meteoroid sizes of 0.3 m. consider bigger meteoroids and craters. The dependence of crater diameter (D) on projectile size Meteoroids of different composition differ not only by and atmosphere pressure is given in Fig. 1b for H chondrite strength but also by bulk densities, ablation energy, and heat meteoroids. For example, the present atmosphere begins to transfer coefficients. We adopt the heat transfer coefficients reduce the crater size (compared to an atmosphereless case) found for Earth by Golub et al. (1996) for H chondrite (OC) only for projectiles smaller than about 0.5 m, but if in a past and iron meteoroids, which are extrapolated here to martian atmosphere of 300 mbar, the effect sets in for projectiles atmosphere densities. Ablation increases importance as size closer to 10 m in size. decreases, and the possible variation of ablation coefficients The resulting crater SFDs are given in Fig. 2. The main by 2–3 times, due to varying atmosphere composition, does result is that the departures from the normal or “production not change the crater distribution essentially, especially for function” SFD would not be easily detectable in crater counts large meteoroids (1 m and larger). unless atmospheric pressures exceeded 30 or even 100 mbar. For carbonaceous chondrites (CC), we use coefficients The NH log differential plots shows this depletion of small for OCs, assuming that evaporation alone will not differ craters most vividly, and Fig. 2 also illustrates that the essentially for these substances. Observational data (see smoothing inherent in the cumulative plot tends to mask this below) indicate a larger value of the ablation coefficient effect. In the most dense atmosphere under consideration (which is equal to the ratio of heat transfer coefficient to (1000 mbar), no impact craters are formed with D <26 m due ablation energy and drag coefficient) for CCs than for the to the low terminal velocity. OCs. We suppose that this difference may be caused by other physical mechanisms integrated into ablation (detachment of FRAGMENTATION THRESHOLD small grains, quasi-continuous fragmentation, etc). We will consider our ablation efficiency for C chondrites as a low Fragmentation of the bolides adds more drastic effects boundary and estimate its influence on the results. than mere deceleration and ablation. Different ways exist to We consider different surface pressures (ps), from 1 up to estimate the conditions for meteoroid breakup in the 1000 mbar. The fraction of initial body energy released on the atmosphere. Most of these approaches model the breakup

Fig. 1. a) Fraction of initial kinetic energy delivered to the ground (Eground) as a function of projectile diameter (Dp) for different atmosphere pressures (labeled in mbar); b) diameter of crater (D) as a function of projectile diameter (Dp), assuming chondrite densities and no breakup. For small objects, drag and ablation result in low impact velocity and departure from the normal scaling laws. 910 O. Popova et al.

Fig. 2. Size-frequency distributions predicted on Mars for consideration of deceleration and ablation alone (not fragmentation) for different atmospheres (labeled in mbar). Two different styles of SFD plot are shown (see section on Crater Distribution): cumulative plot (cumulative 2 2 craters/km larger than D; left) and log-incremental plot (NH = craters/km in each 2 interval in D; right). under aerodynamic loading, and different relations between generally found that larger rock masses are weaker than small meteoroid strength and breakup loading have been suggested ones due to the prevalence of fractures and inhomogeneities. (see Svetsov et al. [1995] for review). Of course, occasionally, a large, strong, homogeneous rock Very limited data on meteoroid strengths are known. mass may be found, but, generally, the concept is useful and Empirical values of the apparent strength (σa) derived from argues against models where a giant meteoroid of ordinary bolide observations may be used along with strengths chondrite composition is assumed necessarily to enter the estimated from properties of meteorites. Some authors (for atmosphere with an effective bulk strength equal to that of a example, Hills and Goda [1993]) used the strength (σa) values hand specimen from a museum. There is no universally derived from meteorites (σa ~100–500 bar for chondrites, σa accepted value for the power exponent (α), but it may be ~2000 bar for irons), and estimated σa ~10 bar for comet estimated as about 0.1–0.5 for stony bodies (Svetsov et al. debris with ice removed. However, note that in nature the 1995). Given a spherical meteoroid’s effective strength, the 2 effective strength of a large specimen tends to be lower than condition for breakup may be written as 0.365 ρaV = σten, that of its smaller constituent volume units because of effects where ρa is atmospheric density (Tsvetkov and Skripnik such as large-scale fractures. We use a strength scaling law 1991). This strength scaling law permits us to successfully (see below) to estimate the strength of big bodies based on the describe the fragmentation of Sikhote Alin and Benešov strengths of smaller samples. Meteorites demonstrate great meteoroids (Nemtchinov and Popova 1997; BoroviËka et al. scatter in the measured strength (Tsvetkov and Skripnik 1991; 1998). Atmospheric fragmentation has been discussed by 2 see Svetsov et al. [1995] for review). The average values of Foschini (2001). He discards the relation of ρaV = σa and the tensile strength of small, less fractured chondrite samples regards models as inconsistent with observed high meteorite (about 10 g in mass) may be estimated as 300–350 bar. The strengths. However, this relation is used for defining the strength decreases as body size increases, according to apparent strength (σa), and we associate the low apparent statistical strength theory (Weibull 1951), consistent with the strengths of initial breakup events with fractured states of the presumed history of parent body collisional fragmentation meteoroids, as discussed. that produced the meteoroids themselves. The effective Observational data demonstrate that most bolides display strength is estimated as fragmentation. According to Canadian bolide Network observations (Halliday et al. 1996), some fragmentation is σ = σ (m /m)α (6) s s common at all heights below 55 km. where σ and m are the effective strength and mass of the Objects entering planetary atmospheres belong to larger body, σs and ms are those of tested specimen, and α is a different taxonomic types. According to several independent scale factor. This concept is partly empirical; in nature, it is methods (Ceplecha et al. 1998), 5 main groupings of fireballs Bolides in the present and past martian atmosphere 911 can be distinguished among the larger Earth-entering Nemtchinov et al. (1997), and some results are shown in meteoroids. The groupings differ in their ability to penetrate Table 1. Here, Er is the energy of the radiation impulse, η is the atmosphere. Ceplecha et al. (1998) proposed fractions of the luminous efficiency assumed for estimates of the initial bodies in the following groupings at the top of the atmosphere: kinetic energy (Eo) (Nemtchinov et al. 1997), M0 is the initial irons = 3%, ordinary chondrites (Ceplecha group I) = 29%, mass, V0 is the initial velocity, Hm is a characteristic altitude carbonaceous chondrites (Ceplecha group II) = 33%, regular of the event, σa is the estimate of aerodynamic pressure cometary material (Ceplecha group IIIA) = 26%, and weak leading to breakup. Projectile diameters (Dp) in Table 1 cometary material (Ceplecha group IIIB) = 9%. assume a meteoroid density of 3 g/cm3 for simplicity. The apparent strength (σa) of 80 Prairie Network Velocities of 8 SN bolides are known due to infrared (henceforth, PN) bolides (relatively small bodies of 2–2000 positional data or eyewitness data. For 5 events, the velocity kg) was estimated by Ceplecha et al. (1993) with the help of was estimated during analysis by Nemtchinov et al. (1997). the gross-fragmentation (trajectory analysis) method. This Characteristic fragmentation altitudes are usually associated study revealed that 38% of them were evidently fragmented with the height of maximum luminosity and are close to 30 during flight, while 36% were unclassified due to insufficient km. Estimating that breakup occurs several km higher observations. Possibly, about 60% of PN bolides (smaller (Popova and Nemtchinov 2002), one may roughly estimate 2 than 1 m in size) fragment during flight. All bodies marked as the breakup loading as ρaV . The value of breakup pressure fragmented were disrupted under apparent loading <12 bar. causing formation of vapor and small fragments cloud was Half of them were fragmented under loading <3.5 bar. Based found to be about 20–50 bar with a large scatter. on his analyses of density, ablation efficiency, and other data, Data on some other observed meteoroids for which data Ceplecha et. al. classified these bodies as being of type I or II, of breakup is known do not contradict to this estimate. For the i.e., ordinary or carbonaceous chondritic composition. Based Pribram meteorite the breakup loading was in the range 10–50 on this work, we assume that some stony bodies may be bar (Bronshten 1983). The Lost City meteoroid was disrupted disrupted at low pressure loading. Among PN bodies studied in several stages (Ceplecha 1996) and the last breakup (H ~22 by Ceplecha et al. (1993), 4 meteoroids survived without km) occurred under loading of about 25 bar (Ceplecha 1996; fragmentation up to 15 bar, and 1 meteoroid survived as Popova 1997). The Peekskill meteoroid fragmented under single body up to 50 bar. These represent stronger classes. loading of about 7 bar (Brown et al. 1994). The flash on light Several PN bolides were analyzed by radiative radius curve Innisfree bolide took place at about 35 km altitude technique (Nemtchinov et al. 1994). This method allows us to under loading of about 18 bar (Halliday et al. 1981). All these estimate the moment of meteoroid breakup into a cloud of bodies were ordinary chondrites. The breakup and bright vapor and small fragments, which rapidly expands and creates flash, and correspondingly intense energy release, occurred flashes on the light curve. This type of fragmentation is more under relatively high-pressure loading (higher than the 12 bar common at relatively low altitudes (40–20 km) under higher result found by Ceplecha et al. [1993]). loading (Popova and Nemtchinov 1996; BoroviËka et al. Meteoroid fragmentation is often a multistage process. 1998; Nemtchinov et al. 1997). The corresponding meteoroid More detailed study of some European Network (EN) and SN strength is about 20–40 bar (Popova 1997). bolides (Marshall Islands, Greenland, Benešov, Moravka) Both methods of breakup analysis—gross fragmentation suggests that the first fragmentation occurs at high altitudes and radiative radius technique—were used in studying the (50–60 km) under pressure loading of a few bars, similar to large Benešov bolide (Dp ~1.2 m) and showed multistage that found by Ceplecha et al. (1993). If the meteoroid is large disruption of this meteoroid. The radiative radius approach enough, first-stage fragments penetrate deeper into the revealed two fragmentation points at altitudes of 40 and 24 atmosphere without essential deceleration and are fragmented km under loading of about 25–30 and 95 bar (BoroviËka et al. once more. The number of second-stage fragments may be 1998). The presence of these breakup events was confirmed large enough that intense energy release results. Breakup by direct observation of fragments during the flight. The pressures causing intense flashes on light curves of relatively dynamics of this meteoroid suggested a third, high-altitude big meteoroids appear to be about 20–50 bar, although we breakup event under loading of 0.5–1 bar. Falls of meteoritic must remain aware of the possibility of breakup under either fragments were predicted for this fireball, but none were smaller or larger loading. found, possibly due to the complex landscape of the fall site. In spite of the low strength of carbonaceous chondrite Apparently, this may have been a pre-fractured object when it meteorites, there are not yet any data demonstrating their entered the atmosphere, beginning to breakup at around 1 bar, different behavior during flight. The analysis done by and then producing strong fragments that needed 25 to 95 bars Ceplecha et al. (1993) does not distinguish carbonaceous and for further breakup. ordinary chondrites by their strength. The difference is seen The next data set about behavior of large meteoroids in only in the ablation coefficient. However, useful data come Earth’s atmosphere is provided by the Satellite Network (SN). from the large Tagish Lake bolide, which produced These data (Tagliaferri et al. 1994) were partially analyzed by carbonaceous chondrite meteorite fragments (Hildebrand et 912 O. Popova et al. (km) 4.5–0 m Mars H g (bar) 2 V a ρ <5–1754–100 4.5 <4, 130–230 24?, 0 0 <7, 20–40 10, 0 = 100–400 a σ f h d g (km) , 25 c j m 43303334, 213434 <930 10–30 <8, >100 12–30 <12046?, 28–25 20–21 4.5, 0 33-21 0 <200 4.5 4.5 0 H Earth g est est est est , 30.5 est est b f (km/s) o 29 e (m) V p 0.9–1.21.71.7 133.2–5 25 36.26.8 15.8 28–30 15 6–10 37 35 8.5 <3 7 e b e e g e (ton) D 36 o (kt) M o E a (%) η (kt) r E = ordinary chondrite; I iron. 15 Apr. 198815 Apr. 1 Oct. 1990 1.704 Oct. 19911 Feb. 1994 0.5729 May 1994 0.14 19943 Nov. 11 4.39 0.09016 Dec. 1994 9.7 0.56 0.0086 8.49 Oct. 1997 12.59 Dec 1999 8.0 8–9 0.045 5.9 3–5 9.77 Jul 1999 0.064 0.9 3118 Jan 2000 0.6–2.523 Apr 2001 7.5 25–45 –14 Jan 1999 0.26 0.07–0.3 3–5 7.8 70–200 1.17 May 19919 Oct 1992 1.2 20 2.5–3 2–140 40014 Aug 1992 3.5–5 0.01 0.25–17 0.6 9.17 Apr 1959 1.1–4.5 0.8 – – 10.4 70–200 – 0.5–2.26 May 2000 48–50 10.4 2.37 Feb. 1977 6.3 – 15–20 <50 3.5–-5 6.112 Feb. 1947 0.006 <40 2.85 10.6 8 – – – 8 – 11.5 – 15–20 15–20 24 5.6 0.16 – ?(200–400) 50–200 – 500 5–6.3 – – ?(1–3) – 0.1 2–4 – ?(0.9–1.2) –? (18) – 3.5–13 1.1–1.4 –? (18) ~10 28.5 1–3 0.4–1 28.8 200–500 21 1–5 0.6–0.9 1.9 0.9–1.2 ?(<20) 0.1–0.02 – 0.9–1.5 0.4–0.2 ?(50–70) 13.5 37, 24 22 14.7 20.9 14 0 12–15 25, below 0 >120 13–22, 36, below below 41, 44–25 10, 0 28–10 60–70 36, below 20–30 >4 12–15 50–300 3–200 0 <8.5 <10, 8.5 16 <21 0 i, j h (OC) f k

p, h (I) (CC) d r (OC) 15 June 1994 0.0031 4.93 0.063 1–3 h b b b b, c b b b b h (OC) (OC) m (OC) q l o (OC) ka et al. 2001 n ka et al. 1998. Ë Ë ibram ¯ 94350 (SN) Greenland (SN) N. Zealand (SN) 01113 (SN) 88106 (SN) 90274 (SN) 91277 (SN) 94032 (SN) 94149 (SN) 94307 (SN) 94166 (SN) Event Date (SN) Yukon Pacific Region Peekskill Mbala P Moravka(SN) Innisfree Sikhote-Alin El Paso (SN) Benešov Brown et al. 1994. Nemtchinov et al. 1997. Hildebrand et al. 1999. Pedersen et al. 2001. release. USAF press Pack et al. 1999. Jenniskens et al. 1994. Bronshten 1983; Ceplecha 1961. Borovi Halliday et al. 1981. CC = carbonaceous chondrite; OC McCord et al. 1995. Popova and Nemtchinov 2000. Ceplecha et al. 1999. Nemtchinov and Popova 1997. Also known as Tagish Lake meteorite. Also known as Tagish Brown et al. 2001. Borovi Table 1. Data of large meteorites in Earth’s atmosphere. meteorites in Earth’s 1. Data of large Table a b c d e f g h i j k l m n o p q r Bolides in the present and past martian atmosphere 913

al. 2000) and had Dp ~3–5 m (Popova and Nemtchinov 2000). subject to fragmentation according to strength scaling laws It was catastrophically disrupted at an altitude above 25 km (Equation 6, using α ~0.2 to 0.1 and referring to the Sikhote- (apparent strength [σa] ~20–40 bar), according to SN data, or Alin meteorites). possibly an altitude of 37 km (σa ~3–10 bar), according to visual observations. These data imply strengths similar to the FRAGMENTATION EFFECTS IN THE LIQUID-LIKE ordinary chondrite producing the St. Robert bolide, which had (“PANCAKE”) MODEL Dp ~1.2 m (Nemtchinov et al. 1997), Hfragm. ~36 km (Brown et al. 1996), and σa ~11 bar. The strength also appears similar Earth’s observational data show that for the biggest to that of the ordinary chondrite Moravka meteorite, which bolides (20–2000 kg), two main types of fragmentation occur. had Dp ~1 m, Hfragm. ~50 to 30 km, and σa ~5 to 50 bar The first is disruption into several large pieces moving (BoroviËka et al. 2001). separately, which may have their own separate histories of Aerodynamic forces on these objects depend mainly on further fragmentation. In the second type, which we consider the atmosphere density and the shape, structure, and other in this section, initially formed fragments move together properties of meteoroids, and, to a lesser extent, on the deeper into the atmosphere and continue their breakup. If the atmospheric chemical composition. Except at the smallest time between fragmentations is smaller than the time for sizes, ablation is less important than fragmentation, which, in fragment separation, all the fragments move as a unit, and a turn, depends mainly on the strength of the meteoroid. So, a swarm of fragments and vapor penetrates deeper, being cosmic body with given pre-atmospheric properties will deformed by aerodynamical loading, like a drop of liquid. decelerate and fragment in the martian atmosphere similarly This liquid-like or “pancake” model assumes that the to one in the Earth’s atmosphere, roughly at levels where the meteoroid breaks up into a swarm of small bodies, which density of the martian atmosphere is the same as that of continues their flight as a single mass with increasing terrestrial air. Thus, to check our theoretical simulations for pancake-like cross-section. This approach was proposed and present-day Mars, one may simply use observational data for developed by Grigorjan (1979), Zahnle (1992), Chyba the case of the Earth but with altitudes decreased by about 30 (1993), Chyba et al. (1993), and Hills and Goda (1993). km. The data on the characteristic altitude deduced above the Numerical simulations of the liquid-like fragmentation under Earth, and also converted to Mars, are given in Table 1. aerodynamic loading show very complicated behavior due to Before 1994, 14 meteoroids with sizes of the order of 1 m the development of instabilities at the boundary (cf., were observed photographically (Ceplecha 1994a, b). Five of Adushkin and Nemtchinov 1994; Svetsov et al. 1995; them (about 30%) had end heights higher than 45–50 km Nemtchinov et al. 1999b; and references therein). Here, we altitude and revealed maximum luminosity at 90–60 km use a semi-analytical approach similar to that of the altitudes. Such high-altitude events generally correspond to pioneering works mentioned above but with some the weakest bodies. One of these events, the Šumava bolide, modifications (Popova and Nemtchinov 1996; details given was studied in detail (BoroviËka and Spurný 1996; by Popova [1997]). The most intense flashes on the light Nemtchinov et al. 1999c). It was disrupted under loading of curves of the largest terrestrial bolides, at the altitudes of 25– about 0.2–1 bar. These bodies were classified as Ceplecha’s 40 km, are well described by this model (Nemtchinov et al. type III (i.e., cometary bodies) because of the apparent very 1997; BoroviËka et al. 1998). Slightly different equations low strengths, high ablation ability, and small bulk density. exist for velocities of radius growth in literature (for review We note that Šumava-like meteoroids of 5000 kg or smaller see Svetsov et al. [1995]). We assume that the velocity of would not reach the ground on present-day Mars. radius increase (u) may be written as follows Nevertheless, larger meteoroids of similar structure and strength would penetrate to the surface and form craters. ukV= ρa ⁄ ρm (7) Additional modeling of such weak and probably volatile-rich bodies should be pursued. where V is the velocity of the body, ρm is the density of the To summarize this brief review of apparent strength of body, ρa is the atmosphere density, and k is constant. A entering bodies: 1) cometary bodies are fragmented at the heavily fragmented body is treated as a cloud of small apparent strength of 0.1–1 bar; 2) carbonaceous chondrites fragments and vapor. The value of k is chosen as k ~0.3; this and ordinary chondrites show a big scatter in apparent value proved to be the best in the modeling of the Benešov strength (Table 1), probably due, in part, to their pre- bolide light curve (BoroviËka et al. 1998) and also is close to atmospheric collision history and condition of internal the value found in numerical simulations of Crawford (1996) fractures. We assume 1, 5, and 25 bar as their apparent and Ivanov et al. (1997). strengths, with 25 bar corresponding to the best solution for The maximum possible increase of radius of the pancake- the maximum intensity of radiation of the bolide; 3) we like swarm of material is an open question. Some theoretical consider iron meteoroids as either having very large strength considerations suppose the radius may increase about 2–3 (and no fragmentation) or (perhaps, if pre-fractured) being times (for example, Hills and Goda [1993]), whereas an 914 O. Popova et al. increase of radiative radius of 3–7 times and more is observed formation and crater scaling law. Other scaling laws (see in bolide light curve analysis. We assume that the vapor cloud Melosh [1989] for review) and the adoption of another cannot increase more than five times and estimate that further terminal velocity necessary for explosive crater formation increase of maximal allowed radius does not change the could change results by about a factor of 2. energy release essentially. The difference in the resulting As the atmosphere density increases, the Dcrit values for crater diameters created by these uncertainties in the pancake different strength H chondrite bodies are close to each other, model of the expanding meteoroid mass is estimated to be no and precise values of meteoroid strengths become more than 10–30%. insignificant in these cases. We treat fragmentation by assuming that breakup starts In the Earth-like case of ps = 1000 mbar, we find that as soon as the aerodynamic loading equals the effective or fragmentation (coupled with the pancake model assumption) apparent strength. We consider several values of apparent causes the disappearance of hypervelocity impact craters strength, 1, 5, and 25 bar, in the range obtained by smaller than D ≅ 200 m, similar to the value of D ≤100 to observations. A comparison of energy fraction released on the 300 m that is seen on Earth itself. This cutoff drops to 32 m planetary surface by non-fragmented and fragmented H for ps = 100 mbar; but, in this case, sub-meter-sized bodies hit chondrite meteoroids is given in Fig. 3a; a comparison of the ground before fragmenting pressure is achieved and hold pancake models for two different values of strength (1 and 25 enough energy to form 4–8 m craters. Thus, from the bar) is given in Fig. 3b. The fragmentation creates a threshold cratering record alone, distinguishing the 100 mbar case from and shift to bigger meteoroid sizes in the energy release the present-day case at MGS/MOC resolution would be curves if the surface pressure exceeds 10 mbar. For dense difficult, but cratering under ps >300 mbar atmosphere would atmospheres (ps ~100–1000 mbar), the energy fraction show a dramatic paucity of craters D = 80 m, compared to the released does not vary much with apparent strength. For less present. dense atmospheres (ps ~1–30 mbar), including the present Corresponding crater SFDs are given in Fig. 4 and regime, the stronger bodies begin to reach the ground without dramatically show the loss of small stony meteorite-caused breaking up. The difference between the present results and craters for atmospheres in the pressure range of ps >30–100 the final column of Table 1, which predicts breakup events for mbar and even ps = 10 mbar for very weak objects. We use a the martian atmosphere, is caused by the higher entry velocity liquid-like model of fragmentation with the strength scaling of terrestrial bolides. For a given atmosphere and ps, a critical law Equation 6, and corresponding columns are included into crater diameter (Dcrit) exists below which no high-velocity Tables 2 and 3 as α = 0.25 and 0.5. The results found with this craters are formed. These critical crater diameters are given in scaling law are close to that obtained with constant apparent Table 2. Under the present atmosphere, Dcrit appears to be 0.5 strength. The specimen mass and strength are adopted to be to 4.5m for H chondrite bodies with strength 25 to 1 bar. The 10 g and σs = 330 bar for H chondrites. The value α ~0.25 precise value of Dcrit and the corresponding size of the appears permissible for meteoroids similar to the SN objects projectile depend on the assumed criterion for crater (Popova and Nemtchinov 2002).

Fig. 3. The fraction of initial kinetic energy delivered to the ground as a function of projectile diameter, showing an H chondrite: a) first assumed to be affected only by drag and ablation (no fragmentation) and secondly with pancake model of fragmentation; b) different assumed apparent strengths.

Table 2. The boundary size of impact craters. H H H H H H Carbonaceous Carbonaceous Carbonaceous ps chondrite chondrite chondrite chondrite chondrite chondrite chondrite chondrite chondrite Comet Iron Iron mbar no breakup σa = 25 bar σa = 5 bar σa = 1 bar α = 0.25 α = 0.5 σa = 25 bar σa = 5 bar σa = 1 bar σa = 1 bar no breakup α = 0.2 1 0.1 0.1 0.1 0.1 0.1 0.1 0.16 0.16 0.16 0.22 0.09 0.09 6 0.5 0.5 0.5 0.5, 4.5 0.5 10.5 0.7 0.7 6 8 0.3 0.3 10 0.7 0.7 0.7 6.6 0.7 0.7 1 1 8.6 11.7 0.5 0.5 30 1.7 1.7 14.4 15.6 1.7 1.7, 16 2.3 18.8 20.3 27.5 1.3 1.3 100 4.4 4.2, 32.3 37.8 38.8 4.4, 36 39 5.5, 41 48.4 49.9 66 3.2 3.2 300 10.4 82 86 87 86 88 104 109 110 143 7.5 7.5, 55 1000 26.4 201 205 207 206 207 246 252 254 312 19 153

Table 3. The size of projective forming boundary crater size given in Table 1. H H H H H H Carbonaceous Carbonaceous Carbonaceous ps chondrite chondrite chondrite chondrite chondrite chondrite chondrite chondrite chondrite Comet Iron Iron mbar no breakup σa = 25 bar σa = 5 bar σa = 1 bar α = 0.25 α = 0.5 σa = 25 bar σa = 5 bar σa = 1 bar σa = 1 bar no breakup α = 0.2 1 0.003 0.003 0.003 0.003 0.003 0.003 0.006 0.006 0.006 0.013 0.0015 0.0015 6 0.02 0.02 0.02 0.02, 0.5 0.02 0.02 0.035 0.035 0.9 1.7 0.01 0.01 10 0.03 0.03 0.03 0.75 0.03 0.03 0.05 0.05 1.4 2.8 0.015 0.015 30 0.08 0.08 1.9 2.2 0.08 0.08, 2.2 0.16 3.6 4 8 0.045 0.045 100 0.3 0.3, 5.4 6.5 6.7 0.3, 6.2 6.8 0.6, 9.5 11.6 12 24 0.14 0.14 300 0.8 17.4 18.4 18.7 18.4 18.8 30.5 32.6 33 62 0.4 0.4, 7.8 1000 2.6 54.7 56 56.5 56.4 56.8 93 95.6 95 168 1.3 28.4 916 O. Popova et al.

Fig. 4. Crater SFDs for pancake-like fragmentation model applied to H chondrites, showing losses of small craters for different atmospheres. NH gives the number of craters of diameter (D) (meters) in each 2 -incremental log D bin (see Hartmann [1999] for further description of this type of plot). The curves represent different atmospheric pressures in millibars, as labeled. The top (1 mbar) curve corresponds approximately to the absence of atmospheric effects.

We must consider the smallest crater sizes expected from Observational data allow us to determine the ablation different classes of meteoroids to interpret not only data from coefficient for much of the meteoroid trajectory (Ceplecha et future missions but also effects of impact gardening by the al. 1999), but its velocity dependence is not known. smallest impactors. Minimum sizes of projectiles striking the According to Ceplecha et al. (1999), the ablation coefficient surface at >500 m/s are given in Table 3. For these small varies with composition by as much as a factor of 10, is meteoroid sizes, ablation plays an essential role and we have maximal for cometary bodies (~0.1–0.2 s2/km2), and is used an ablation model. Vasavada et al. (1993) considered minimal for ordinary chondrites (~0.014 s2/km2) on average. ablation and found that, for the current atmosphere, all Hörz et al. (1999) favored a value at the higher end of this meteoroids in the range of Dp ~0.4 to 20 cm are completely range, while we have used values near the lower end. We ablated. As a result, they predicted the smallest crater size to possibly underestimate the ablation efficiency, and our results be about 3 m, but we believe that the ablation efficiency in concerning boundary meteoroid size given in Table 3 could that work is overestimated because of terrestrial experience. be increased as much as 1.5–2 times. Terrestrial data show that a fraction of cm-sized bodies We found that under current conditions, the boundary (Bolide Network bodies) penetrates below 30 km altitude on size of impact crater may be 0.3 m and is formed due to the the earth and would hit the martian surface. For example, impact of ~1 cm iron body. The uncertainty of the minimum according to Halliday et al. (1996), there were 46 probable crater diameter estimates may be about a factor of 2. meteorite drop objects among 754 fireballs with terminal Tables 2 and 3 include meteoroids similar to 3 mass >0.1 kg (and initial mass about 0.3–1300 kg [mainly 1– carbonaceous chondrites with ρm = 2 g/cm , assuming 5 kg]). apparent strengths of 25, 5, and 1 bar. Due to the bigger effect For martian conditions, even more meteoroids should of deceleration, the boundary values of projectile and crater survive down to the ground due to lower average entry size are bigger than for H chondrite meteoroids. We also 3 velocity. The lower the entry velocity, the lower the efficiency consider cometary bodies (with ρm ~1 g/cm ) and apparent of ablation (Golub’ et al. 1996). Theoretical consideration strength of 1 bar. All critical cometary cutoff diameters are demonstrated that the ablation coefficient depends on size, shifted to bigger sizes for a given pressure. Note that our size height, velocity, and meteoroid composition (Golub’ et al. estimates for C chondrites and comets should be considered 1996). For cm-sized bodies, this result is an ablation as low boundary (see also the discussion in the section on coefficient of about 0.003–0.023 s2/km2, depending on Influence of Atmospheric Deceleration and Albation on altitude and velocity (BoroviËka et al. 1998). The stony Cratering). Moravka bolide ablation coefficient is also as low as 0.003 s2/ We were interested in comparing the smallest predicted km2 (BoroviËka et al. 2001). crater sizes with the MGS/MOC resolution limit for good Bolides in the present and past martian atmosphere 917

crater counts, around 11 m. The smallest values of Dcrit and Dp correspond to nonfragmented iron bodies. We also predict formation of 30–50 cm impact craters under current atmospheric conditions due to the impact of 1–4 cm stony and iron bodies. This is comparable to the results of Hörz et al. (1999), whose ablation impact model also predicts smallest craters in the “sub-meter” range, formed from strong stones and irons a few cm in size. Figure 5 shows data from Table 2. Fragmentation has no influence on strong, small stony bodies in the current atmosphere. The minimum size of weak H chondrite impactors (σa = 1 bar) is about 50 cm, and the smallest impact crater in our model is about 4.5 m. For cometary bodies, our assumptions yield a meteoroid diameter of about 2 m, forming 8 or 9 m craters, just below the MGS/ MOC resolution limit. For a denser atmosphere of ps = 100 mbar, the smallest impact crater size is about 3 m for an iron meteoroid. Undisrupted stony bodies also may form craters of about 4–5 m in size. For still denser atmospheres, the minimum impactor body size increases to about 5–10 m for all weak or Fig. 5. Summary diagram showing the expected sizes of the smallest fragmented stony bodies with a minimum crater size of 30–50 explosion craters (D, meters) on Mars for different atmospheres, for each meteorite class. For the present atmosphere, the smallest craters m. Thus, during (Noachian) periods when the atmosphere are around 5–10 m for weak meteorites and a few centimeters for exceeded a few hundred millibars, there should have been no irons and strong stones. craters below 30–50 m in size formed by stony and cometary bodies and only a few decameter-sized craters formed by the suggested that the velocity (u) of the fragment repulsion can relatively infrequent irons. The crater deficiency would be be described by Equation 7. They analyzed terrestrial crater difficult to detect, however, due to the populations of fields and found the constant (k) to be 0.14 to 1.22. subsequent small craters formed under the later, thinner Artemieva and Shuvalov (1996, 2001) modeled the atmospheric conditions. interaction of two fragments by direct 3D gas-dynamical simulations and found that the coefficient (k) in Equation 7 is PROGRESSIVE FRAGMENTATION MODEL AND about 0.45 for two equal cubic fragments. If the fragments are CONSEQUENCES ON CRATERING not equal, the lateral velocity of the smaller fragment will be higher. In the case of a meteoroid initially disrupted into 13 or Modeling the actual disruption of the body in the 27 cubic fragments with cracks between them (Artemieva and atmosphere is the biggest problem for the liquid-like model. Shuvalov 2001), the lateral velocity that defines the debris This model assumes movement as a collective swarm and cloud radius can be written in the form of Equation 7, but the does not take into account that some parts of the body may be coefficient (k) is higher: ~1. In their latest paper (Artemieva stronger than other parts, surviving to the ground and and Shuvalov 2001), the evaporation of fragments was taken producing meteorites. Thus, we introduce a progressive into account but it did not substantially change the mechanical fragmentation model, which assumes that separate fragments forces and coefficient (k). Note that their result was obtained form at the moment of breakup and spread laterally. These only for ordinary chondrites. Volatile-rich meteoroids need to fragments continue their flight separately from each other and be studied. can be disrupted during further flight. Both types of Comparison of lateral fragment velocities with Earth fragmentation—progressive fragmentation and “liquid-like” bolide and meteorite data shows that the value of (k) should fragmentation—are observed among terrestrial bolides. be at least ~1 or even more (BoroviËka et al. 1998). We start Progressive fragmentation has been considered in a with k ~1 in our estimates and increase it in certain cases, number of works since 1956 (Levin 1956, 1961; Fadeenko depending on relative momentum among the fragments. We 1967; Baldwin and Sheaffer 1971). In most cases, the successfully used these lateral velocity estimates to describe fragmentation into a number of fragments is described the Sikhote-Alin crater field and Benešov bolide fragments without taking into account the lateral spreading of fragments. dynamics (Nemtchinov and Popova 1997; BoroviËka et al. However, Passey and Melosh (1980) considered the 1998). aerodynamical interaction of fragments due to the The progressive fragmentation model can be used if the compression of gas between them in the bow shock waves number of fragments is not too large and if the fragments are and the force that bow shocks exert on each other, and they well separated. If the time of fragment interaction is greater 918 O. Popova et al. than the time interval between two fragmentations, the chondrites have produced decimeter-sized, low-impact- fragments demonstrate collective behavior, as in the liquid-like velocity specimens, while a number of larger objects, like the model (see Svetsov et al. [1995] for review). In an ideal case, Tunguska and Greenland bolides, apparently produced no fragments of a body larger than a certain size would not have recoverable specimens that large. Possibly, they enter the time to separate and would follow the liquid-like model, atmosphere with pre-existing fracture planes or granular making one crater, while below that size, the fragments would structure that cause them to fragment into very small separate, and the smaller bolide’s behavior would follow the constituent pieces. Very small fragments do not make progressive fragmentation model, making several craters. We explosion craters at all because they fall to the ground at low find that for chondritic bodies with the exponent α = 0.25, the terminal velocities affected by drag or get blown away in the progressive fragmentation model may be used with a size of Dp atmosphere altogether. To treat the craters produced by the ~≤10 m in the current martian atmosphere. The 10-m projectile fragments from breakups, we need to know the size of the would form a crater of D ~90–230 m in the case of 6–100 mbar largest fragment, the size distribution of the fragments, and atmospheres, according to the pancake model. The range of the impact velocities of those fragments. This requires predicted transitional crater sizes, where single craters may improved modeling in future work, but we attempt a start to give way to strewn fields of craters, is sensitive to the preliminary treatment here. adopted model of breakup. We cannot yet determine what As before, we assume the following meteoroid fractions: model is better around this size, so we will note the differences 3% irons, 29% ordinary chondrites, 33% carbonaceous in resulting pictures under these two models. Note also that the chondrites, and 35% cometary. First, we will not include lateral velocities of the fragments are important in determining fragmentation. The total SFDs of craters from the undisrupted the dimensions of strewn fields formed in the breakups. meteoroids are given in Fig. 6a. Note that in atmospheres Separated fragments may even form single craters in the case denser than 100–300 mbar, the deceleration and ablation of small dispersion of the fragments. begin to cause deviations of the martian SFD from the lunar Given the atmospheric density and strength law, the SFD at crater diameters smaller than 100–500 m. This is transitional crater size, i.e., the maximum crater size produced similar to our conclusion from Fig. 2 but is now much more by the fragments in the progressive fragmentation model, is general because we have found that all classes, not just constrained to some degree. The value is determined by the chondrites, produce craters. maximal fragment size surviving in a given atmosphere, We start this discussion with the liquid-like (pancake) which does not depend on initial meteoroid mass, according model, which calls for all fragments to hit the ground together to our law of effective strength versus size. In dense in one area and make a single crater. atmospheres (ps ~300–1000 mbar), small separated fragments To estimate the fragmentation influence over a range of are decelerated much more effectively than a massive single strengths, we consider the following meteoroid strengths body, and because of atmospheric drag, no hypervelocity parameters. For irons, we use the specimen strength of σs = impact craters are formed by the fragments, throughout the 440 bar for a 1 kg specimen size and scaling of α = 0.2 (see range of model validity. Thus, in dense atmospheres above discussion in the Fragmentation Threshold section). For 300 mbar, fragmentation processes should cause a dramatic chondrites, we use the apparent strength = 25 bar (that is decrease in crater number (N) in SFD below crater sizes of similar to specimen strength of σs = 330 bar for a 10 g about 200–300 m, similar to the paucity of <300 m explosion specimen size with α = 0.25; carbonaceous chondrites σa = 5 craters on Earth. The predictions of both fragmentation bar; cometary bodies σa = 1 bar). We use the pancake model models coincide in that sense. and find evident fragmentation, especially for denser atmospheres (Fig. 6b). CRATER SFD CAUSED BY TOTAL The effects of fragmentation on the SFD are seen even METEOROID POPULATION for the present atmosphere and are more pronounced in denser ones (ps >30 mbar). Under the present atmosphere, the At this point, we are facing the problem of how the main cratering contribution (D ~1–1000 m) comes from meteoroid breakup and production of fragments affects the ordinary chondrites, but as the atmosphere pressure increases crater SFD observed on the ground. While we lose the (ps >30 mbar), stony bodies are increasingly lost by breakup. meteoroid itself, we must take into account the craters added At 100 mb, irons make the main contribution to cratering in by the pieces of the fragmenting meteoroid. What are the the D ~4–200 m range. Although stony bodies are still realistic sizes of the fragments? If an ordinary terrestrial rock producing craters down to 30–40 m in size, their contribution is shattered with low energy density, the largest pieces may be to total SFD in D ~30–200 m is smaller than that of iron half the size of the original. But, as energy density increases, meteoroids. Even above the crater size resolved by MGS/ the largest surviving pieces are smaller (Hartmann 1969). MOC (D ~10 m), the log incremental plot (NH) shows a Atmospheric breakup is a high energy density event, in this dramatic cutoff of small craters as ps increases from 100 to sense, and we note in Table 1 that several meter-sized 300 mbar and above (Figs. 5 and 6b). Bolides in the present and past martian atmosphere 919

Fig. 6. Crater SFD predicated by adding all classes of meteorites, from weak bodies to irons: a) in an absence of fragmentation; b) including fragmentation even for irons. Plotted as in Fig. 4.

We also investigated the case where lower strengths are effect of fragment-caused craters added to the SFD must exist, assumed for most meteoroids (irons—the same as in the and these effects will probably be found among decimeter- or previous case; OC σa = 5 bar; CC σa = 1 bar; comets σa = 0.1 meter-scale craters below the present 11 m limit of MGS/ bar). These weak bodies are effectively fragmented by present MOC crater resolution. atmosphere, and craters 3–100 m in size are formed mainly by How do we search for atmospheric cutoff effects and irons. At 100 mbar, the SFD is close to the case of the strong possible strewn fields of small craters? One important factor bodies, considered above, except for meter-sized craters. should be taken into account. Small craters are lost due to dust Small stony meteoroids are able to form these craters if σa = infill, dune deposits, etc. (Hartmann 1971; Hartmann and 25 bar. At ps >100 mbar, the cratering efficiency is only Neukum 2001), complicating any claims of detection of slightly dependent on the precise values of stony/cometary deficiencies due to loss of small bolides. These factors are meteoroid strengths in the considered strength range. probably least important for craters formed on the young What are the main effects of fragmentation on the final hard-rock lava flow surfaces that have been detected on Mars SFD of craters observed on Mars? We have described how the (Hartmann and Berman 2000; Hartmann and Neukum 2001), liquid-like model may underestimate the fragmentation and and these surfaces would be ideal to conduct further tests of cratering influence for decameter bodies. The turndown the atmospheric cutoff effects on small craters, from about 0.1 boundary on SFD will be more dramatic, i.e., shifted to bigger m to 10 m in size, during future missions. crater sizes, if one takes into account progressive fragmentation. In the present atmosphere, the fragments of DETECTING PAST ATMOSPHERIC VARIATIONS the broken weak meteoroids would make clusters of high- velocity craters at very small crater sizes (probably meter These discussions raise intriguing potential for using the scale or smaller), adding to the crater population that would cratering record to reveal past variations in the atmospheric be predicted from the unaltered production function SFD. In pressure of Mars. We have mentioned 3 main effects that hypothetical denser past atmospheres, still bigger meteoroids could arise during past periods of high atmospheric density: breakup. One might expect bigger fragment-caused craters, 1) dense atmospheres deplete small craters (4 previous but the fragments would be subject to greater pressure loading sections). For example, during any period when the and would break into smaller pieces, as implied by our atmosphere had periods with pressure over 300 mbar, no adopted law of strength versus size. Moreover, they would hypervelocity craters will exist smaller than about 80 m, face increased drag in the denser atmosphere and tend to hit except for the irons and strongest stones, which are a fairly the ground too slowly to make normal explosion craters. In small fraction of the total (Table 2 and Figs. 4 and 6b). the other direction, as we approach ps = 0 mbar, eventually no However, it will not be easy to detect such variations from the fragmentation and no fragment-caused craters exist. cratering record because the subsequent (present) thin- Therefore, one can see that at some atmospheric pressure, and atmosphere condition leads to an overlying population of depending on meteoroid strength distribution, a maximum small craters, which are very numerous because they lie in the 920 O. Popova et al. steep part of the SFD; 2) dense atmospheres produce more changed on very short timescales of less than 1 Myr. The clusters of small craters from atmospheric events recent pressures seem very likely to have risen above the 100 (Fragmentation Threshold section and the 2 sections before mbar levels widely postulated for early Mars. At pressures the current section). We expect the craters to be small, e.g., <100 mbar, the atmospheric meteoroid losses are primarily tens of meters in scale and spread over clusters up to about a represented by crater losses in the (D) range of 10 to 40 m for km in scale, not unlike the terrestrial strewn-field case (see the various stony meteorite types. This is near the cutoff in next section). This effect should be preserved in cratering resolution for MGS/MOC images and would be hard to records; and 3) dense atmospheres break up stones, leading to document in current imagery. Furthermore, these craters dominance of irons as creators of mid-sized, 10–100 m-scale resaturate in only about 10 Myr to 200 Myr, respectively, craters (as on Earth), while the present martian atmosphere according to the cratering rate data above, so the putative high would allow dominance of stones as source of these craters pressure periods would have to have reached many tens of (previous section). This effect should be observable but mbar, been fairly long-lived, and recently ended to leave a would require sophisticated ground based sampling. detectable signature in loss of very small craters. According The use of crater populations to study ancient to Fig. 6b, recent transient higher-pressure episodes at <100 atmospheres leads to several specific cases of interest. mbar would also be hard to detect through crater clusters due to fragmentation events. Noachian Higher Pressure Periods Low Pressure Periods That the Noachian atmospheric pressure was greater, perhaps up to hundreds of mbar has been widely suggested. Under the current 6 mbar pressure, hypervelocity craters, The crater cutoff we find at 300 mbar is D ~80–100 m as even produced by irons, would be formed at sizes down to D mentioned above, and even for 1 bar, it rises only to D = 200 ~0.3 m (Fig. 5). Hörz et al. (1999) found a similar result and m. A population of craters due to irons and strong stones asserted the detection of spall craters 0.25 m across on rocks might reach smaller sizes (D ~20 m). If such an atmosphere in Pathfinder photos. As noted by Hörz et al. (1999), rock dwindled by the end of the Noachian or Hesperian periods surfaces offer much better preservation of such small craters (perhaps causing the end of those periods), then the loss of than loose or lightly cemented martian soils. Plausibly, that atmosphere would have occurred by 2000 to 3500 Myr obliquity variations might have created periods of lower ago, according to the chronology of Hartmann and Neukum atmospheric pressure than the current 6 mbar. During these (2001). However, according to the modern crater production periods, rocks on the surface might be hit by even smaller and gardening rates developed by Hartmann and Neukum meteoroids that would otherwise be blocked by the 6 mbar (2001), Ivanov (2001), and Hartmann et al. (2001), craters in atmosphere. Through future rover missions or human the size range of 40 m to 200 m reach saturation under landings, spall marks and “zap pits” of this sort might be modern conditions in as little as only about 200 Myr to as sought in surface rocks to confirm atmospheric variations. much as 3000 Myr, respectively. Therefore, detecting the This effect might also be detected by comparing the highest turndown in the population of small craters created during a elevation sites with low elevation sites. Noachian high-pressure period would be difficult. However, recent observations of Mars increase the GARDENING EFFECTS probability that some ancient surfaces of Mars have been buried by sedimentary layers and recently exhumed (Malin If the long term average of the atmospheric pressure and Edgett 2000) and that these surfaces may preserve ancient during Amazonian times has been <100 mbar, our results crater populations (Greeley et. al. 2001; Hartmann et al. 2001, indicate that the cratering by abundant small bodies pp. 49–51). On such ancient, preserved surfaces, behavior of guarantees a certain degree of gardening effects, although, the the original small-crater population might be difficult to lack of micrometeorite “sandblasting” means that the regolith confirm because of obliteration effects, but tell-tale clustering so produced would be coarser than on the moon. Hartmann et of craters due to dense-atmosphere fragmentation events al. (2001) discussed such gardening in more detail and might be observable from orbital imagery, and composition showed that the geometry of crater coverage and saturation signatures of the impactors might be observable on the require martian regolith production regardless of the absolute ground. ages of the surface units. martian winds would mobilize the finest debris, and the removal of fines from coarse regolith Recent Higher Pressure Periods may be a factor in producing the boulder-strewn landscapes seen by the first 3 landers. Plausibly, obliquity variations or volcanic outbursts As for more ancient times, we have shown that the might have increased martian surface pressures in more hypothetical denser atmosphere would have resulted in the recent times. Malin et al. (2001) argue that the atmosphere has loss of still more small craters. Nonetheless, saturation would Bolides in the present and past martian atmosphere 921 again guarantee gardening effects. Direct crater counts in the existing uplands show that saturation was at least approached at crater sizes around 45–64 km. Probably, smaller craters also reached saturation but have been lost subsequently due to erosion effects (Hartmann et al. 2001). Thus, megaregolith should have been produced on Noachian Mars down to depths of km scale. Our results in this paper suggest that, under a Noachian atmosphere of a few hundred mbar, impact cratering would not occur below decameter scale, and this would ensure that the early martian megaregolith would be substantially coarser than the lunar example. The coarse early megaregolith would probably have served as a very efficient sink for early martian water, which may exist today as large masses of ground ice mixed into the coarse, upland fragmental layer.

MARTIAN CRATER CLUSTERS

During examination of Viking pictures, numerous, seemingly isolated clusters of 500 m scale craters, in patches 5 to 20 km across, were noted on Mars (Hartmann and Engel 1994). An example is shown in Fig. 7. Hartmann and Engel suggested that these might represent breakups of unusually weak, cometary bodies in the high atmosphere. Such a hypothesis would require lateral spreading of fragments at speeds on the order of 300 m/s to attain the observed spreading during atmosphere passage, as judged by u = (cluster radius/atmosphere flight time). Such lateral spreading speeds were indeed observed among small, kg-scale fragments of the Benešov (BoroviËka et al. 1998) and Moravka (BoroviËka et al. 2001) bolides. However, our current investigations of the lateral spreading of fragments do not allow such high velocities among the larger, crater- forming fragments of the bolide disruptions we are considering for Mars. In the current model, the lateral velocity depends on the altitude and entry velocity (Equation 7). For an entry speed of 20 km/s, the lateral velocity is about 27 m/s for breakup of a stronger body at 10 km altitude. These figures do not allow enough time for the creation of such large clusters as are observed on Mars. We are currently investigating various effects that might produce the observed clusters, including: 1) explosive gas production that might drive apart weak, ice-rich fragments making up a comet; 2) Fig. 7. a) East portion of cluster of overlapping 700 m-scale in MGS image 12–014325, at latititue –20°S, longitude 182°W; b) Viking disruption of cometary bodies by tidal forces, impacts, or context mosaic showing surrounding area, next to Ma’adim Vallis. other processes at some distance from Mars, before entry; 3) The cluster seems isolated, without an obvious recent parent crater ejection from martian craters of secondary blocks, which that could act as a source of secondaries. This type of cluster appears disperse during flight upward through the atmosphere and fall to have too great a width to be accounted for by our modes of back at random locations, making clusters; and 4) dislodging fragmentation of primary meteoroids but might involve isolated blocks of secondary ejecta lofted at near-escape velocity. of fragmenting blocks of secondary ejecta from impacts on Phobos or Deimos. in size and scattered over regions of the order of 100 m in Our ongoing work with the progressive fragmentation diameter. A possible example is shown in Fig. 8. model applied to the present atmosphere predicts some We intend to report on the phenomena of clusters of large fragmentation among modest-sized weak bodies, which craters, as well as clusters of small craters, in more detail in should produce clusters of small impact craters tens of meters our planned second paper. 922 O. Popova et al.

Fig. 8. This MGS/MOC image shows what appears to be a cluster of 10 m-scale craters spread over a few hundred meters. Unlike Fig. 7, this appears to match our predicated product of meteoroid fragmentation in the current atmosphere.

CONCLUSIONS lower atmospheric pressure, perhaps caused by obliquity variations. The smallest craters expected under current atmospheric As can be understood from this paper, reality is more conditions on Mars have diameters the order of 0.3 m due to complex than the existing models. To improve the modeling iron meteorites that survived atmospheric passage. They and reach a better understanding of Mars, new work is needed might best be detected on martian rocks, as discussed by Hörz on subjects such as: 1) improved fragmentation modeling to et al. (1999). The smallest martian craters due to stony reconcile the liquid-like and progressive fragmentation meteoroids range from 0.5 to 6 m in diameter, depending on models; 2) a better understanding of the ablation parameter, the strength of the meteoroids, and the smallest craters due to especially for volatile-rich bodies; 3) a better modeling of the hypothetical weak icy or icy/carbonaceous cometary lateral separation of fragments, especially among volatile- meteoroids would be about 8 m across. rich bodies where gas production may affect the interaction of The proposed presence of a complete production shock waves and lateral forces; 4) a better modeling of the function size distribution of craters down to meter or sub- fate of the fragments produced by disruptions, taking into meter scale guarantees some impact gardening effects on the account their size distributions, terminal velocities, and evolution of older surfaces. This may also be a factor in resulting craters; and 5) higher resolution imagery of selected generating martian dust and obliterating distinctive ancient surfaces (including ground imagery of smooth rock surfaces) deposits such as lakebed evaporates. to search for crater depletion and/or “zap pit” effects. Fragmentation influences the crater formation process on Mars, but primarily in hypothetical denser past atmospheres. Acknowledgments–We thank Professor Johannes Geiss and In the present atmosphere, only the weakest bodies, with the International Space Science Institute (ISSI) in Bern, strength of ~1 bar, would fragment. As summarized in the Switzerland, for hosting a workshop in which we were able to previous section, and discussed in more detail in our work together to prepare this paper. We also thank Daniel forthcoming paper on crater clusters, the progressive Berman at PSI for valuable assistance in finding or processing fragmentation model predicts clusters of small craters with a MGS/MOC and Viking images of crater clusters and Boris diameter (D) of order 1–10 m, spread over a few hundred Ivanov at IDG for valuable discussions. We acknowledge meters. Therefore, small crater clusters formed by our helpful critiques from S. J. Weidenschilling, S. Kortenkamp, predicted contemporary breakup of ordinary stones and irons E. Pierazzo, other PSI staff, and two anonymous reviewers for under ~30 to ~300 mb may be hard to distinguish from the Meteoritics & Planetary Science. The MGS images are small clusters formed by weak stones in the present courtesy of NASA, Jet Propulsion Laboratory, and Malin atmosphere. Craters much smaller than 0.3 m (such as “zap Space Systems. O. Popova and I. Nemtchinov are partially pits” in rocks) would be diagnostic of earlier periods with supported by NASA international project NRA 98–055–08– Bolides in the present and past martian atmosphere 923

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